In particular Euclid exploited a logical weapon known as reductio ad absurdum, or proof by contradiction. The approach revolves around the perverse idea of trying to prove that a theorem is true by first assuming that the theorem is false. The mathematician then explores the logical consequences of the theorem being false. At some point along the chain of logic there is a contradiction (e.g., 2 + 2 = 5). Mathematics abhors a contradiction, and therefore the original theorem cannot be false, i.e., it must be true.
